Classification by statistics A coherent beam of constant intensity is described by Poisson statistics If/when an intensity fluctuation is present  Super-Poissonian statistics Non-classic light  Sub- Poissonian distribution Not classic light Perfectly coherent light Partially coherent, uncoherent, thermal emission L’osservazione di statistica Poissoniana e super-Poissoniana può essere spiegata dalla teoria classica ondulatoria Statistica sub-Poissoniana è la firma inequivocabile della natura quantistica della luce Fotone Vediamo ora un modo diverso di analizzare le caratteristiche della luce in base alla correlazione al secondo ordine F. De Matteis Quantum Optics

Coherence measurements in astronomy Michelson stellar interferometer Varing d and measuring fringe visibility at screen centrum: Max from star center minimum from D/2 if D/L≈l/d }Cancel 1920 Mount Wilson Red giant Betelgeuse in Orion constellation l/d=500nm/6m~10-7 rad D/L~2,2x10-7 rad Increase d to improve resolution Mirror vibrations cancel the interference figure F. De Matteis Quantum Optics

Coherence measurements in astronomy Hambury-Brown Twiss Correlate light intensity from two different points of wavefront The average of the products (Second order corr.) varies in the two cases 2 detectors collect light from two different angles  different area of the wavefront are incoherent Sirio Star l/d=400nm/188m~2x10-9 rad D/L~3,3x10-8 rad 2 detectors collect light from two close angles  same area of the wavefront (still coherent) F. De Matteis Quantum Optics

Intensity interferometry experiment Originate from astronomy studies. The interpretation of the results raised several conceptual difficulties. The principles of the experiment were tested in laboratory Each detector measures the fluctuation of the beam intensity (AC coupling) For chaotic beam, the measured signal is 1 for t<<tc and drop to 0 for t>>tc For choerent light, one gets 0 at any value of delay F. De Matteis Quantum Optics

Degree of second-order coherence for chaotic light For classic light (chaotic or coherent) F. De Matteis Quantum Optics L6/5

Hanbury-Brown Twiss experiments: quantum picture Single photon-counting configuration Event=«time elapsed between D1 count and D2 count is t » Photon flux with long intervals between photons. Each photon either hits D1 or D2 Bunched stream of photons Considerando la natura quantistica della luce, fotoni che viaggiano, si giunge a risultati molto diversi che nel caso classico di fluttuazione di intensità F. De Matteis Quantum Optics

Classification by coherence Coherent light Photon statistic Poissonian with intervals between photons completly random  Probability for stop pulse independent by t Bunched light Photon statistic SuperPoissoniana with intervals between photon very tight Probability for stop pulse high for small t Anti-bunched light Intervals between photons very regular Close to start pulse low probability of stop Then increase Sub-Poissoniana   anti-bunching Not exactly the same (Zou&Mandel, PhysRevA 1990) F. De Matteis Quantum Optics

Experimental demonstrations of antibunching Signal from single emitter  antibunched beam Kimble,Dagenais,Mandel, PhysRevLett 1977 A single atom must be in the visual field of measuring device (slit) Excitation of InAs on GaAs quantum dots Sub-ideality due to finite response time of the photon counting system Michler et al, Science 2000 F. De Matteis Quantum Optics

Single photon sources Quantum criptography, eg. Emission of a single photon following a trigger pulse Subsequent emission needs a subsequent trigger Low quantum eff , T=5K Yuan Science 2002 GaAs-LED P-i-N InAs quantum dots are inserted in the GaAs intrinsic layer. The QD size distribution produces the l spread F. De Matteis Quantum Optics